What is a PRP ?
A PRP is a probable prime number, a number that nobody knows how to prove
or disprove its primality.
Here are some criterions that can be used to recognize these numbers
:
- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N
should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3.
N should pass the strong test in base b.
- or more (if someone has got an idea) !!!
Submit your PRPs
See the Top discoverers
See the Latest PRPs
Search by form
Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
8001 | 44^49524+43 | 81391 | Norbert Schneider | 06/2014 |
8002 | (3*2^270368-1)/13 | 81389 | Lelio R Paula | 02/2014 |
8003 | 19548^14563+14563^19548 | 81384 | Hans Havermann | 05/2020 |
8004 | (2^270337+1130)/2 | 81380 | Stefano Morozzi | 01/2020 |
8005 | 27405^932+932^27405 | 81377 | Hans Havermann | 05/2020 |
8006 | 19396^15683+15683^19396 | 81375 | Hans Havermann | 05/2020 |
8008 | (10^81363+719)/9 | 81363 | Serge Batalov | 12/2014 |
8007 | (734^28393-1)/733 | 81363 | Serge Batalov | 08/2020 |
8009 | (10^81353+449)/9 | 81353 | Serge Batalov | 12/2014 |
8010 | 14^70978-89 | 81350 | Lelio R Paula | 11/2015 |
8011 | 11^78108-2040 | 81342 | Enzo Doria | 12/2012 |
8012 | 7*10^81327-57 | 81328 | Robert Price | 06/2020 |
8013 | (7*10^81328-79)/9 | 81328 | Robert Price | 01/2021 |
8014 | 19102^18065+18065^19102 | 81315 | Hans Havermann | 07/2020 |
8015 | 3^170400-58 | 81302 | Lelio R Paula | 12/2015 |
8016 | (17*10^81300-131)/3 | 81301 | Robert Price | 12/2017 |
8017 | 10^81297+36991 | 81298 | Patrick De Geest | 06/2013 |
8018 | 10^81297-57 | 81297 | Robert Price | 05/2011 |
8019 | (2^270063+3206)/2 | 81297 | Stefano Morozzi | 01/2020 |
8020 | 19359^15826+15826^19359 | 81296 | Hans Havermann | 06/2020 |
8021 | 2^270055-113047 | 81295 | Enzo Doria | 07/2014 |
8022 | 18^64759-55 | 81291 | Lelio R Paula | 11/2015 |
8023 | (2^269987+1)/3 | 81274 | H.&R. Lifchitz | 10/2000 |
8024 | (31^54493-1)/30 | 81268 | Alexander Zhirkov | 10/2010 |
8025 | (2^270059-1)/540119/6481417/7124976157756725967 | 81265 | Dario Alpern | 09/2014 |
8026 | (194^35521-1)/193 | 81263 | Serge Batalov | 08/2020 |
8027 | 20722^8343+8343^20722 | 81258 | Hans Havermann | 07/2020 |
8028 | (2^269922+3574)/2 | 81255 | Stefano Morozzi | 01/2020 |
8029 | 21310^6497+6497^21310 | 81249 | Hans Havermann | 07/2020 |
8030 | (16392^19273-1)/16391 | 81225 | Serge Batalov | 08/2020 |
8031 | 2^269819-4597 | 81224 | Yves Minet | 03/2019 |
8032 | (2^269816+7)/424901 | 81218 | Lelio R Paula | 12/2012 |
8033 | 23470^2887+2887^23470 | 81217 | Hans Havermann | 05/2020 |
8034 | (23*10^81214+1)/3 | 81215 | Serge Batalov | 06/2009 |
8035 | (2^269720+3778)/2 | 81194 | Stefano Morozzi | 01/2020 |
8036 | (17*2^269720+1)/303 | 81193 | Lelio R Paula | 07/2012 |
8037 | 56^46441-55^46441 | 81188 | Robert Price | 10/2013 |
8038 | 2^269664+177 | 81177 | Lelio R Paula | 06/2012 |
8039 | (13*2^269665-1)/185 | 81177 | Lelio R Paula | 02/2014 |
8040 | 21642^5615+5615^21642 | 81144 | Hans Havermann | 07/2020 |
8041 | 2^269539-112249 | 81140 | Enzo Doria | 06/2014 |
8042 | ((2*170026-3)*3^(170026-1)+1)/4 | 81128 | Robert Price | 01/2015 |
8044 | (2^269495-5)/9 | 81126 | Lelio R Paula | 12/2012 |
8043 | 1239^26228+26228^1239 | 81126 | Norbert Schneider | 10/2019 |
8045 | 2^269490-3623 | 81125 | Yves Minet | 10/2009 |
8046 | (55459*2^269444+1)/35 | 81114 | Lelio R Paula | 06/2014 |
8047 | 19554^14065+14065^19554 | 81113 | Hans Havermann | 06/2020 |
8048 | (2^269417+78557)/5257 | 81099 | Lelio R Paula | 12/2012 |
8049 | 4*5^116011-7 | 81089 | Lelio R Paula | 10/2014 |
8050 | (2^269349+2366)/2 | 81082 | Stefano Morozzi | 01/2020 |
8051 | (2^269303+2946)/2 | 81068 | Stefano Morozzi | 01/2020 |
8052 | 6*10^81060+53 | 81061 | Robert Price | 05/2020 |
8053 | 7*10^81058+79 | 81059 | Robert Price | 02/2017 |
8054 | 2^269236-109907 | 81049 | Enzo Doria | 04/2014 |
8055 | (2^269182+1870)/2 | 81032 | Stefano Morozzi | 01/2020 |
8056 | (2^269179+3006)/2 | 81031 | Stefano Morozzi | 01/2020 |
8057 | (8*10^81029-11)/3 | 81030 | Erik Branger | 03/2014 |
8058 | 19749^12668+12668^19749 | 81025 | Hans Havermann | 05/2020 |
8059 | 3*10^81021+7 | 81022 | Erik Branger | 11/2013 |
8060 | 6^104115+103 | 81018 | Lelio R Paula | 12/2015 |
8061 | 2^269120+1869151 | 81014 | Enzo Doria | 05/2016 |
8062 | 5^115901+12 | 81012 | Lelio R Paula | 10/2015 |
8063 | (2^269072+3610)/2 | 80999 | Stefano Morozzi | 01/2020 |
8064 | (2^269083-9)/320369 | 80997 | Lelio R Paula | 12/2012 |
8065 | (5*10^80992-179)/3 | 80993 | Robert Price | 10/2020 |
8066 | 2*10^80981-49 | 80982 | Robert Price | 09/2020 |
8067 | (2^269002+1614)/2 | 80978 | Stefano Morozzi | 01/2020 |
8068 | 17^65810-20 | 80976 | Lelio R Paula | 11/2015 |
8069 | 20^62236-23 | 80971 | Lelio R Paula | 01/2016 |
8070 | 2^268974-112181 | 80970 | Enzo Doria | 06/2014 |
8072 | L(387433) | 80969 | Renaud Lifchitz | 11/2003 |
8071 | V(387433) | 80969 | Serge Batalov | 03/2015 |
8073 | 22732^3645+3645^22732 | 80965 | Hans Havermann | 06/2020 |
8074 | (2^268957+602)/2 | 80964 | Stefano Morozzi | 01/2020 |
8075 | (2^268955-509203)/5 | 80963 | Lelio R Paula | 12/2012 |
8076 | 19485^14284+14284^19485 | 80958 | Hans Havermann | 05/2020 |
8077 | (87398^16384+1)/65537 | 80957 | Lelio R Paula | 11/2011 |
8078 | 329^32160+32160^329 | 80954 | Norbert Schneider | 11/2014 |
8079 | 19678^12973+12973^19678 | 80937 | Hans Havermann | 02/2020 |
8080 | (2^268864+3558)/2 | 80936 | Stefano Morozzi | 01/2020 |
8081 | 2^268859-159 | 80935 | Lelio R Paula | 05/2012 |
8082 | (2^268841-lucasV(1,2,268841)+1)/2 | 80929 | Mike Oakes | 11/2016 |
8084 | 2^268827+5775 | 80925 | Lelio R Paula | 07/2013 |
8083 | 2^268824-110255 | 80925 | Enzo Doria | 05/2014 |
8085 | (2^268824+1902)/2 | 80924 | Stefano Morozzi | 01/2020 |
8086 | 2^268798-1868321 | 80917 | Enzo Doria | 04/2016 |
8087 | 20613^8420+8420^20613 | 80913 | Hans Havermann | 03/2020 |
8088 | 2^268753-114621 | 80903 | Enzo Doria | 05/2015 |
8089 | 2^268743+1605 | 80900 | Lelio R Paula | 07/2013 |
8090 | 6^103954-139 | 80892 | Lelio R Paula | 12/2015 |
8091 | 10^80883+49 | 80884 | Robert Price | 03/2011 |
8092 | 10^80883-80327 | 80883 | Patrick De Geest | 07/2013 |
8093 | 6^103937+121 | 80879 | Lelio R Paula | 12/2015 |
8094 | 148^37266+147 | 80877 | Norbert Schneider | 12/2018 |
8095 | (26*10^80875-119)/3 | 80876 | Robert Price | 07/2016 |
8096 | (22699*2^268657+1)/6351 | 80875 | Lelio R Paula | 06/2014 |
8097 | (2^268612+2530)/2 | 80860 | Stefano Morozzi | 01/2020 |
8098 | 2^268581-869688105 | 80851 | Lelio R Paula | 05/2016 |
8099 | (11*2^268521-1)/3 | 80834 | Lelio R Paula | 02/2014 |
8100 | 2^268516-249 | 80832 | Yves Minet | 02/2012 |
8101 | 22259^4278+4278^22259 | 80828 | Hans Havermann | 03/2020 |
8102 | 2^268500+16095 | 80827 | Lelio R Paula | 07/2013 |
8103 | 3^169402+100 | 80826 | Lelio R Paula | 12/2015 |
8104 | (2^268495+566)/2 | 80825 | Stefano Morozzi | 01/2020 |
8105 | 9^84698+8^(84698-1) | 80823 | Robert Price | 03/2016 |
8106 | 2^268472-109739 | 80819 | Enzo Doria | 04/2014 |
8107 | (9*2^268454+1)/37 | 80813 | Lelio R Paula | 12/2012 |
8108 | (3*2^268502+1)/377902188435353647 | 80811 | Lelio R Paula | 12/2012 |
8109 | (2^268441+3962)/2 | 80809 | Stefano Morozzi | 01/2020 |
8110 | 134^37987-133^37987 | 80803 | Jean-Louis Charton | 12/2005 |
8111 | 15^68702-76 | 80800 | Lelio R Paula | 11/2015 |
8112 | 2^268408+7 | 80799 | Lelio R Paula | 05/2012 |
8113 | (16095^19207-1)/16094 | 80794 | Serge Batalov | 08/2020 |
8114 | 2^268375+141 | 80789 | Lelio R Paula | 05/2012 |
8115 | 12^74856-47 | 80784 | Lelio R Paula | 11/2015 |
8116 | 2^268346+524287 | 80781 | Paul Underwood | 08/2018 |
8117 | 9*10^80777-41 | 80778 | Robert Price | 08/2020 |
8118 | (10868^20011-1)/10867 | 80764 | Serge Batalov | 08/2020 |
8119 | 6^103770-107 | 80749 | Lelio R Paula | 12/2015 |
8120 | (751^28081-1)/750 | 80748 | Serge Batalov | 08/2020 |
8121 | 3^169224-62 | 80741 | Lelio R Paula | 12/2015 |
8122 | p(16866)#/2+64 | 80741 | Robert Price | 03/2017 |
8123 | 5^115502-72 | 80733 | Lelio R Paula | 10/2015 |
8124 | (2^268154+2262)/2 | 80723 | Stefano Morozzi | 01/2020 |
8125 | (2^268156+1290)/2 | 80723 | Stefano Morozzi | 01/2020 |
8127 | 2^268079-1927 | 80700 | Yves Minet | 10/2009 |
8126 | (2^268078+2514)/2 | 80700 | Stefano Morozzi | 01/2020 |
8128 | 2^268028+117 | 80685 | Lelio R Paula | 05/2012 |
8129 | 121^38738+120 | 80683 | Norbert Schneider | 01/2015 |
8130 | (3^169097-8)/835 | 80677 | Lelio R Paula | 12/2012 |
8131 | (2^267956+1810)/2 | 80663 | Stefano Morozzi | 01/2020 |
8132 | 19359^14666+14666^19359 | 80656 | Hans Havermann | 12/2019 |
8133 | 2^267918+67 | 80652 | Lelio R Paula | 05/2012 |
8134 | (89*10^80650-179)/9 | 80651 | Robert Price | 11/2017 |
8135 | (2^267914+2094)/2 | 80650 | Stefano Morozzi | 01/2020 |
8136 | (2^267894+2202)/2 | 80644 | Stefano Morozzi | 01/2020 |
8137 | (302*10^80638+13)/9 | 80640 | Robert Price | 01/2017 |
8138 | 3^169004+2660 | 80636 | Lelio R Paula | 12/2015 |
8139 | 2^267860-112859 | 80634 | Enzo Doria | 06/2014 |
8140 | 2^267828-110705 | 80625 | Enzo Doria | 05/2014 |
8141 | (2956^23227-1)/2955 | 80611 | Serge Batalov | 08/2020 |
8142 | (2^267752+2602)/2 | 80602 | Stefano Morozzi | 01/2020 |
8143 | 2^267743+12705 | 80599 | Lelio R Paula | 07/2013 |
8144 | (22*10^80595+23)/9 | 80596 | Robert Price | 03/2015 |
8145 | (2^267712+2358)/2 | 80590 | Stefano Morozzi | 01/2020 |
8146 | (2^267685+854)/2 | 80581 | Stefano Morozzi | 01/2020 |
8147 | 2^267674-51 | 80578 | Lelio R Paula | 05/2012 |
8148 | (86*10^80571-41)/9 | 80572 | Robert Price | 11/2015 |
8149 | (2^267637+2454)/2 | 80567 | Stefano Morozzi | 01/2020 |
8150 | 20452^8693+8693^20452 | 80564 | Hans Havermann | 02/2020 |
8151 | 2^267612-1965 | 80560 | Lelio R Paula | 07/2013 |
8152 | 2^267553+4097 | 80542 | Lelio R Paula | 07/2013 |
8153 | 7^95276-8 | 80518 | Robert Price | 01/2014 |
8154 | (15185*2^267457-1)/47829 | 80513 | Lelio R Paula | 04/2015 |
8155 | 6^103467+163 | 80513 | Lelio R Paula | 12/2015 |
8156 | 20283^9314+9314^20283 | 80506 | Hans Havermann | 02/2020 |
8157 | (2^267387+2294)/2 | 80492 | Stefano Morozzi | 01/2020 |
8158 | (7*10^80490+143)/3 | 80491 | Robert Price | 04/2016 |
8159 | 19887^11152+11152^19887 | 80490 | Hans Havermann | 01/2020 |
8160 | (2^267348+3810)/2 | 80480 | Stefano Morozzi | 01/2020 |
8161 | 86^41597-85^41597 | 80470 | Robert Price | 04/2015 |
8162 | 13^72237+30 | 80468 | Lelio R Paula | 11/2015 |
8163 | 17^65389+14 | 80458 | Lelio R Paula | 11/2015 |
8164 | 423^30634+30634^423 | 80456 | Norbert Schneider | 05/2017 |
8165 | (2^267257+470)/2 | 80453 | Stefano Morozzi | 01/2020 |
8166 | 2^267232+105 | 80445 | Lelio R Paula | 05/2012 |
8167 | (298*10^80442+11)/3 | 80444 | Robert Price | 11/2020 |
8168 | 22101^4360+4360^22101 | 80437 | Hans Havermann | 02/2020 |
8169 | 11^77237-3072000 | 80435 | Enzo Doria | 01/2013 |
8170 | 20696^7689+7689^20696 | 80422 | Hans Havermann | 01/2020 |
8171 | (2^267149+2562)/2 | 80420 | Stefano Morozzi | 01/2020 |
8172 | 21321^5908+5908^21321 | 80411 | Hans Havermann | 02/2020 |
8173 | (13100^19531-1)/13099 | 80411 | Serge Batalov | 08/2020 |
8174 | 2^267116-459959 | 80410 | Enzo Doria | 06/2015 |
8175 | 38715!2+8 | 80406 | Robert Price | 01/2015 |
8176 | 19579^12786+12786^19579 | 80406 | Hans Havermann | 02/2020 |
8177 | (2^267017+1)/3 | 80380 | H.&R. Lifchitz | 09/2000 |
8178 | (2^267006+1134)/2 | 80377 | Stefano Morozzi | 01/2020 |
8179 | 24273^2048+2048^24273 | 80376 | Hans Havermann | 01/2020 |
8180 | (2^266989+734)/2 | 80372 | Stefano Morozzi | 01/2020 |
8181 | (2^266989+1850)/2 | 80372 | Stefano Morozzi | 01/2020 |
8182 | (13427^19471-1)/13426 | 80372 | Serge Batalov | 08/2020 |
8183 | 2^266968-45 | 80366 | Lelio R Paula | 05/2012 |
8184 | (2^266967+3974)/2 | 80365 | Stefano Morozzi | 01/2020 |
8185 | 20^61768-63 | 80363 | Lelio R Paula | 01/2016 |
8186 | (6253^21169-1)/6252 | 80356 | Serge Batalov | 08/2020 |
8187 | (14005^19381-1)/14004 | 80355 | Serge Batalov | 08/2020 |
8188 | 2^266920-112967 | 80351 | Enzo Doria | 06/2014 |
8189 | (2^266910+2394)/2 | 80348 | Stefano Morozzi | 01/2020 |
8190 | (2^266899+1994)/2 | 80345 | Stefano Morozzi | 01/2020 |
8191 | 8*10^80342+87 | 80343 | Robert Price | 10/2017 |
8192 | (10^80363+1)/11866136004174221950876906463 | 80335 | Anonymous | 10/2020 |
8193 | (2^266861+890)/2 | 80333 | Stefano Morozzi | 01/2020 |
8194 | 12^74428-13 | 80322 | Lelio R Paula | 11/2015 |
8195 | (2^266810+2718)/2 | 80318 | Stefano Morozzi | 01/2020 |
8196 | (2^266800+2886)/2 | 80315 | Stefano Morozzi | 01/2020 |
8197 | (6163^21187-1)/6162 | 80291 | Serge Batalov | 08/2020 |
8198 | 2^266680+27 | 80279 | Lelio R Paula | 05/2012 |
8199 | 2^266630-131 | 80264 | Lelio R Paula | 05/2012 |
8200 | (2^266627+1278)/2 | 80263 | Stefano Morozzi | 01/2020 |
8201 | 2^266598+76819 | 80254 | Enzo Doria | 05/2016 |
8202 | 24463^1908+1908^24463 | 80253 | Hans Havermann | 01/2020 |
8203 | 2^266587+1880633 | 80251 | Enzo Doria | 10/2016 |
8204 | (2^266570+3942)/2 | 80246 | Stefano Morozzi | 01/2020 |
8205 | 2^266541-110049 | 80237 | Enzo Doria | 04/2014 |
8206 | 38635!2-8 | 80222 | Robert Price | 06/2015 |
8207 | (2^266465+986)/2 | 80214 | Stefano Morozzi | 01/2020 |
8208 | 3^168111+168111^3-1 | 80210 | Robert Price | 04/2014 |
8209 | (2^266447+758)/2 | 80209 | Stefano Morozzi | 01/2020 |
8210 | 2^266443+513 | 80208 | Lelio R Paula | 07/2013 |
8211 | (26*10^80200+61)/3 | 80201 | Robert Price | 06/2017 |
8212 | 2^266412-109913 | 80199 | Enzo Doria | 04/2014 |
8213 | (10223*2^266417+1)/45091 | 80199 | Lelio R Paula | 06/2014 |
8214 | 2^266413-4693 | 80199 | Yves Minet | 05/2019 |
8215 | (13737^19381-1)/13736 | 80193 | Serge Batalov | 08/2020 |
8216 | 13^71988+66 | 80191 | Lelio R Paula | 11/2015 |
8217 | 11^77002-4320 | 80190 | Enzo Doria | 01/2013 |
8218 | 19839^11012+11012^19839 | 80187 | Hans Havermann | 03/2020 |
8220 | 18^63879-13 | 80186 | Lelio R Paula | 11/2015 |
8219 | (2^266371+1814)/2 | 80186 | Stefano Morozzi | 01/2020 |
8221 | 2^266368-112295 | 80185 | Enzo Doria | 06/2014 |
8222 | 19217^14880+14880^19217 | 80185 | Hans Havermann | 03/2020 |
8223 | (3^168050+5)/1021454 | 80175 | Lelio R Paula | 10/2012 |
8224 | (2^266324+1386)/2 | 80172 | Stefano Morozzi | 01/2020 |
8225 | (22*10^80167+41)/9 | 80168 | Robert Price | 02/2015 |
8226 | (2^266308+1618)/2 | 80167 | Stefano Morozzi | 01/2020 |
8227 | (34*10^80162-43)/9 | 80163 | Ray Chandler | 12/2010 |
8228 | (2^266276+762)/2 | 80157 | Stefano Morozzi | 01/2020 |
8230 | (38*10^80150-11)/9 | 80151 | Robert Price | 05/2015 |
8229 | (598*10^80149-31)/9 | 80151 | Robert Price | 02/2017 |
8231 | 19^62678-80 | 80150 | Lelio R Paula | 12/2015 |
8232 | (559^29173-1)/558 | 80148 | Serge Batalov | 08/2020 |
8233 | 10^80139+32343 | 80140 | Patrick De Geest | 02/2011 |
8234 | 10^80139-9 | 80139 | Alexander Gramolin | 01/2011 |
8235 | 3^167955-106 | 80135 | Lelio R Paula | 12/2015 |
8236 | 20545^7944+7944^20545 | 80127 | Hans Havermann | 04/2020 |
8237 | 18876^17569+17569^18876 | 80124 | Hans Havermann | 03/2020 |
8238 | (2^266137+3782)/2 | 80115 | Stefano Morozzi | 01/2020 |
8239 | (2^266121+3846)/2 | 80111 | Stefano Morozzi | 01/2020 |
8240 | 22752^3313+3313^22752 | 80093 | Hans Havermann | 03/2020 |
8241 | (197*10^80089-11)/3 | 80091 | Robert Price | 10/2017 |
8242 | 2^265998+75559 | 80074 | Enzo Doria | 04/2016 |
8243 | (2^265999+3290)/2 | 80074 | Stefano Morozzi | 01/2020 |
8244 | 2^265969-109801 | 80065 | Enzo Doria | 04/2014 |
8245 | (2^265956+3378)/2 | 80061 | Stefano Morozzi | 01/2020 |
8246 | (185*10^80051-11)/3 | 80053 | Robert Price | 10/2020 |
8247 | 2^265888-112757 | 80041 | Enzo Doria | 06/2014 |
8248 | (24847^18211-1)/24846 | 80038 | Serge Batalov | 08/2020 |
8249 | 2^265809+1701 | 80017 | Lelio R Paula | 07/2013 |
8250 | gcd(V(957175),5*F(191435)*(F(191435)+1)+1) | 80014 | Serge Batalov | 04/2015 |